Limiting the roll on a rigid body cylinder joint chain
All you really need to do is get rid of the Child Of constraints on all of your bones.

The other thing I did which will improve the accuracy of the simulation, is change the shape of the ridge body collision shapes, so that they are thinner and wider (they can also be much shorter).

In this picture I have the ridge body collision set to "Box", and as you can see it works fine.




For reference here is before and after.